Nash equilibria for a model of traffic flow with several groups of drivers

Traffic flow is modeled by a conservation law describing the density of cars. It is assumed that each driver chooses his own departure time in order to minimize the sum of a departure and an arrival cost. There are N groups of drivers, The i -th group consists of κ i drivers, sharing the same departure and arrival costs ϕ i (t ),ψ i (t ). For any given population sizes κ 1 ,... ,κ n , we prove the existence of a Nash equilibrium solution, where no driver can lower his own total cost by choosing a different departure time. The possible non-uniqueness, and a characterization of this Nash equilibrium solution, are also discussed.

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